Distributional expansions on extremes from skew-normal distribution under power normalization
type: Item
instance of: scholarly article
title: Distributional expansions on extremes from skew-normal distribution under power normalization
zbMATH Open document ID: 1390.62020
author: Sha Jiang
author: Xin Liao
author: Tingting Li
published in: Statistical Papers
publication date: 2018-03-22T00:00:00Z
review text: Let \(X_1,X_2,\ldots\) be a sequence of independent and identically distributed random variables, each having a skew-normal distribution (with parameter \(\lambda\in\mathbb{R}\)) with probability density function given by \[ f_\lambda(x)=2\phi(x)\Phi(\lambda x)\,,\qquad x\in\mathbb{R}\,, \] where \(\phi\) and \(\Phi\) are the density and distribution functions of the standard normal random variable, respectively. The main results of this paper are expansions of the distribution and density functions of \(M_n=\max(X_1,\ldots,X_n)\) under appropriate power normalization, that is, a normalization of the form \(\left(M_n/\alpha_n\right)^{1/\beta_n}\), with appropriate choices of \(\alpha_n\) and \(\beta_n\). The authors also present numerical illustrations of their higher-order expansions, and some comparison with analogous results under a linear normalization of the maximum.
reviewed by: Fraser Daly
Mathematics Subject Classification ID: 62E17
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G70
zbMATH DE Number: 6852088
zbMATH Keywords: higher-order expansion
zbMATH Keywords: power normalization
zbMATH Keywords: maximum
zbMATH Keywords: skew-normal distribution
describes a project that uses: sn
MaRDI profile type: Publication
full work available at URL: s00362-016-0749-8
OpenAlex ID: W2269417211
cites work: Q3703094
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DOI: 10.1007/S00362-016-0749-8
description: scientific article; zbMATH DE number 6852088